A224397 Number of possibilities of getting a prime sum when rolling n six-sided dice.

0, 3, 15, 73, 432, 2466, 12690, 67628, 395896, 2378907, 14778790, 93389066, 562139796, 3163874871, 17458695226, 100299771120, 608013094016, 3788103579016, 23633567094114, 145391247840963, 873481016484060, 5103300936908811, 29074526437910272, 163299878621689106

Offset

0,2

Comments

Possibilities are counted "with repetition", i.e., rolling 2+3 and 3+2 counts as two possibilities. Otherwise said, the probability of getting a prime sum when rolling n six-sided dice, multiplied by 6^n.

Links

Giovanni Resta, Table of n, a(n) for n = 0..120

C. Rivera, Puzzle 684 - Primes in N dice.

Mathematica

a[n_] := Block[{pc}, pc[w_] := n! / Times @@ ((Length /@ Split@w)!); Sum[Total[pc /@ IntegerPartitions[p, {n}, Range@6]], {p, Prime@ Range@ PrimePi[6*n]}]]; Array[a, 20] (* Giovanni Resta, Apr 06 2013 *)

Prog

(PARI) a(n, s=0)=forvec(v=vector(n, i, [1, 6]), isprime(sum(i=1, n, v[i])) && s++); s \\ Illustrative purpose only, impractical for n>>7.

Crossrefs

Sequence in context: A124543 A007142 A357222 * A190010 A151326 A063000

Adjacent sequences: A224394 A224395 A224396 * A224398 A224399 A224400

Keyword

nonn

Author

M. F. Hasler, Apr 05 2013

Extensions

a(11)-a(23) from Giovanni Resta, Apr 06 2013

Status

approved